Whakaoti i te ∫ (from - 015 to 665) of [(-x^2+2x)-(-1+1/2x)] wrt x

$$\int _ { - 015 } ^ { 665 } [ ( - x ^ { 2 } + 2 x ) - ( - 1 + \frac { 1 } { 2 } x ) ] d x$$

Aromātai

$$-\frac{1172330495}{12}\approx -97694207.916666667$$

Ngā Upane Otinga

Hei kimi i te tauaro o -1+\frac{1}{2}x, kimihia te tauaro o ia taurangi.

$$\int _{0\times 15}^{665}-x^{2}+2x+1-\frac{1}{2}x\mathrm{d}x$$

Pahekotia te 2x me -\frac{1}{2}x, ka \frac{3}{2}x.

$$\int _{0\times 15}^{665}-x^{2}+\frac{3}{2}x+1\mathrm{d}x$$

Whakareatia te 0 ki te 15, ka 0.

$$\int _{0}^{665}-x^{2}+\frac{3}{2}x+1\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int -x^{2}+\frac{3x}{2}+1\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int -x^{2}\mathrm{d}x+\int \frac{3x}{2}\mathrm{d}x+\int 1\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$-\int x^{2}\mathrm{d}x+\frac{3\int x\mathrm{d}x}{2}+\int 1\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{2}\mathrm{d}x ki te \frac{x^{3}}{3}. Whakareatia -1 ki te \frac{x^{3}}{3}.

$$-\frac{x^{3}}{3}+\frac{3\int x\mathrm{d}x}{2}+\int 1\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x\mathrm{d}x ki te \frac{x^{2}}{2}. Whakareatia \frac{3}{2} ki te \frac{x^{2}}{2}.

$$-\frac{x^{3}}{3}+\frac{3x^{2}}{4}+\int 1\mathrm{d}x$$

Kimihia te tau tōpū o 1 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$-\frac{x^{3}}{3}+\frac{3x^{2}}{4}+x$$

Ko te tau tōpū tautuhi ko te pārōnaki kōaro o te kīanga i aromātaitia i te tepe tōrunga o te pāwhaitua, tangohia te pārōnaki kōaro i aromātaitia i te tepe tōraro o te pāwhaitua.

$$-\frac{665^{3}}{3}+\frac{3}{4}\times 665^{2}+665-\left(-\frac{0^{3}}{3}+\frac{3}{4}\times 0^{2}+0\right)$$

Whakarūnātia.

$$-\frac{1172330495}{12}$$